Quantum-Mechanical Analysis of Single-Particle Level Density

A quantum-mechanical calculation of the single-particle level (s.p.l.) density $g(\epsilon)$ is carried on by using the connection with the single-particle Green's function. The relation between the imaginary part of Green's function and single-particle wave functions is used separately for the discrete and continuous states. Within the bound-states region the imaginary part of the Green's function is calculated by using the wronskian theorem. The Green's function corresponding to the continuum is written by using the regular and Jost solutions of the radial Schrodinger equation. The smooth part of the rapidly fluctuating s.p.l. density is calculated by means of the Strutinski procedure. The continuum component of the s.p.l. density has rather close values within either exact quantum-mechanical calculations with the Woods-Saxon (WS) potential, or Thomas-Fermi approximation with WS as well as finite-square potential wells, provided that the free-gas contribution is subtracted. A similar trend is obtained by means of the simple FGM formula for the s.p.l. density if the continuum effect is taken into account.